hugeRR: Fitting big ridge regression

Description

Function fits big ridge regression with special computational advantage for the cases when number of shrinkage parameters exceeds number of observations. The shrinkage parameter, lambda, can be pre-specified or estimated along with the model. Any subset of model parameter can be shrunk.

Usage

hugeRR(y, X, Z.name, Z.index, weight = NULL, family = gaussian(link = identity),  lambda = NULL, only.estimates = FALSE, tol.err = 1e-6, tol.conv = 1e-8,  save.cache = FALSE, ...)

Arguments

the vector of response variable.

the design matrix related to the parameters not to be shrunk (i.e. fixed effects in the mixed model framework).

Z.name

file name to be combined with Z.index for the design matrix associated with shrinkage parameters (i.e. random effects in the mixed model framework). The files should be in DatABEL format (see Details).

Z.index

file index/indices to be combined with Z.name. See Details.

family

the distribution family of y, see help('family') for more details.

weight

a vector of prior weights for each of the shrinkage parameters.

lambda

the shrinkage parameter determines the amount of shrinkage. Default is NULL meaning that it is to be estimated along with other model parameters.

only.estimates

logical; TRUE if hat values are to be returned. Default is FALSE and the hat values are not returned.

tol.err

internal tolerance level for extremely small values; default value is 1e-6.

tol.conv

tolerance level in convergence; default value is 1e-8.

save.cache

logical; specify whether internal cache files should be saved for fast future repeating analyses. If TRUE, some R data files will be saved in the current working directory, so that in the future, analyses involving the same cache data can substantially speed up.

...

unused arguments.

Value

phi: estimated residual variance (Non-genetic variance component).
lambda: estimated random effect variance (Genetic variance component). which is proportional to the usual lambda parameter of the ridge regression representing the amount of shrinkage.
beta: fixed effects estimates - subset of model parameters which is/are not shrunk, i.e. those associated with the X matrix.
u: random effects estimates (genetic effects of each marker) - subset of model parameters which are shrunk, i.e. those associated with the Z matrix.
leverage: hat values for the random effects.
hglm: the internal fitted hglm object for the linear mixed model.
Call: how the bigRR was called.

Details

The function does the same job as the bigRR function, but allows huge size of data (the Z matrix) that cannot be loaded into computer memory as a whole. Instead of specifying the entire design matrix for random effects (Z in bigRR), the Z can be split as Z = cbind(Z1, Z2, ..., Zk), and each piece of Z is stored in DatABEL format with file names specified by the arguments Z.name and Z.index. For example (see also Examples), if the genotype data for each chromosome is stored in DatABEL format with file names chr1.fvd & chr1.fvi, ..., chr22.fvd & chr22.fvi, the input argument should be specified as Z.name = 'chr' and Z.index = 1:22.

References

Shen X, Alam M, Fikse F and Ronnegard L (2013). A novel generalized ridge regression method for quantitative genetics. Genetics, 193, 1255-1268.

Ronnegard L, Shen X and Alam M (2010): hglm: A Package for Fitting Hierarchical Generalized Linear Models. The R Journal, 2(2), 20-28.

Examples

Run this code

# --------------------------------------------- #  
#              Arabidopsis example              #
# --------------------------------------------- #  

require(bigRR)
data(Arabidopsis)
X <- matrix(1, length(y), 1)

## Not run: 
# # splitting the genotype data into two pieces and re-saving in DatABEL format
# #
# dimnames(Z) <- list(NULL, NULL)
# Z <- scale(Z)
# matrix2databel(Z[,1:100000], 'part1')
# matrix2databel(Z[,100001:ncol(Z)], 'part2')
# 
# # fitting SNP-BLUP, i.e. a ridge regression on all the markers across the genome
# #
# SNP.BLUP.result <- hugeRR(y = y, X = X, Z.name = 'part', Z.index = 1:2, 
#                           family = binomial(link = 'logit'), save.cache = TRUE)
#                           
# # re-run SNP-BLUP - a lot faster since cache data are stored
# SNP.BLUP.result <- hugeRR(y = y, X = X, Z.name = 'part', Z.index = 1:2, 
#                           family = binomial(link = 'logit'))
# 
# # fitting HEM, i.e. a generalized ridge regression with marker-specific shrinkage
# #
# HEM.result <- hugeRR_update(SNP.BLUP.result, Z.name = 'part', Z.index = 1:2, 
#                             family = binomial(link = 'logit'))
# 
# # plot and compare the estimated effects from both methods
# #
# split.screen(c(1, 2))
# split.screen(c(2, 1), screen = 1)
# screen(3); plot(abs(SNP.BLUP.result$u), cex = .6, col = 'slateblue')
# screen(4); plot(abs(HEM.result$u), cex = .6, col = 'olivedrab')
# screen(2); plot(abs(SNP.BLUP.result$u), abs(HEM.result$u), cex = .6, pch = 19, 
#                 col = 'darkmagenta')
# 
# # create a random new genotypes for 10 individuals with the same number of markers 
# # and predict the outcome using the fitted HEM
# #
# Z.new <- matrix(sample(c(-1, 1), 10*ncol(Z), TRUE), 10)
# y.predict <- as.numeric(HEM.result$beta + Z.new %*% HEM.result$u)
# #
# # NOTE: The above prediction may not be good due to the scaling in the HEM 
# #       fitting above, and alternatively, one can either remove the scaling 
# #       above or scale Z.new by row-binding it with the original Z matrix.
# ## End(Not run)

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